We consider the so-called Drinfeld setting, a function field analogue of some aspects of the theory of modular forms, modular curves and elliptic curves. In this setting Drinfeld constructed families of modular curves defined over a complete, algebraically closed field of characteristic $p.$ We are interested in studying their Weierstrass points, a finite set of points of geometric interest. In this talk we will present some tools from the theory of Drinfeld modular forms that were developed to further this study, some geometric and analytic considerations, and some partial results towards computing the image of these points modulo a prime ideal of the base ring.